Please use this form if you would like to have this math solver on your website, free of charge.

Name:

Email:

Your Website:

Msg:

Scientific Notation

Objective Learn how to write very large and
small numbers in scientific notation and to compare and order
numbers written in scientific notation.

Scientific notation is a useful topic for many applications.
It also provides a great opportunity to reinforce your
understanding of place value in terms of powers of ten.

Very Large and Very Small Numbers

Let's see some very large and very small numbers. A few
examples are listed.

 The mass of the planet Pluto is roughly
12,900,000,000,000,000,000,000 kilograms.

 The number of molecules in a cubic centimeter of oxygen
at standard temperature and pressure is about
602,000,000,000,000,000,000,000.

 A typical cell membrane is about 0.00000001 meter
thick.

 A large virus has a diameter of roughly 0.0000001
meter.

Each of the numbers shown above contains many zeros. Thus, it
may be difficult to read and compare them. However, there is a
notation that can be used to express all of the zeros in a
simple, easy to read form. Consider the following examples.

Example 1

7,000,000,000 (seven
billion)

= 7 Ã— (one billion)

= 7 Ã— 10 9 One billion is
equal to 10 9.

Notice how few symbols are required to write 7 Ã— 10 9
compared to 7,000,000.

Example 2

13,000,000 (thirteen
million)

= 13 Ã— (one million)

= 13 Ã— 10 6 One billion is
equal to 10 6.

= 1.3 10 7 1.3 is one tenth of 13.

Example 3

0.0000056 (fifty-six ten-millionths)

= 5 Ã— (one millionth) + 6 Ã— (one
ten-millionth)

1,000,000 = 10 6 and
10,000,000 = 10 7

= 5 Ã— 10 -6 + 6 Ã—10 -7

Laws of Negative Exponents

= (5 + 6 Ã—10 -1 ) Ã— 10
-6

Factor 10 -6 .

= 5.6 Ã— 10 -6

Key Idea

Every nonzero number can be written as a number greater than
or equal to one and less than ten times a power of ten.

Definition of Scientific Notation

A number that is written as a number between 1 and 10 times a
power of ten is said to be written in scientific notation.

All of the following numbers are written in scientific
notation.

1.2 Ã—10 6

2.4 Ã—10 -5

5.8 Ã—10 18

The following numbers are not written in scientific notation
because the number in front of the multiplication sign is not
between 1 and 10.